@inproceedings{GschreySeifriedKruegeretal., author = {Gschrey, Manuel and Seifried, Marc and Kr{\"u}ger, Luzy and Schmidt, Ronny and Schulze, Jan-Hindrick and Heindel, Tobias and Burger, Sven and Rodt, Sven and Schmidt, Frank and Strittmatter, Andre and Reitzenstein, Stephan}, title = {Boosting the photon-extraction efficiency of nanophotonic structures by deterministic microlenses}, series = {CLEO: 2014}, booktitle = {CLEO: 2014}, publisher = {Optical Society of America}, doi = {10.1364/CLEO_QELS.2014.FF2K.2}, pages = {FF2K.2}, language = {en} } @misc{AmiranashviliBandelowBlomeetal., author = {Amiranashvili, Shalva and Bandelow, Uwe and Blome, Mark and Burger, Sven and Schmidt, Frank and Schmidt, Kersten and Zschiedrich, Lin}, title = {Nanophotonics and nonlinear fiber optics}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and et al.,}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {257 -- 275}, language = {en} } @inproceedings{ThomaSchnauberGschreyetal., author = {Thoma, Alexander and Schnauber, Peter and Gschrey, Manuel and Schmidt, Ronny and Wohlfeil, Benjamin and Seifried, Marc and Schulze, Jan-Hindrick and Burger, Sven and Schmidt, Frank and Strittmatter, Andre and Rodt, Sven and Heindel, Tobias and Reitzenstein, Stephan}, title = {Indistinguishable Photons from Deterministic Quantum Dot Microlenses}, series = {European Conference on Lasers and Electro-Optics - European Quantum Electronics Conference}, booktitle = {European Conference on Lasers and Electro-Optics - European Quantum Electronics Conference}, doi = {10.1364/IPRSN.2015.IS4A.6}, pages = {EA_8_5}, language = {en} } @inproceedings{GschreySeifriedKruegeretal., author = {Gschrey, Manuel and Seifried, Marc and Kr{\"u}ger, Luzy and Schmidt, Ronny and Schulze, Jan-Hindrick and Heindel, Tobias and Burger, Sven and Rodt, Sven and Schmidt, Frank and Strittmatter, Andre and Reitzenstein, Stephan}, title = {Advanced Quantum Light Sources: Modelling and Realization by Deterministic Nanofabrication Technologies}, series = {Integrated Photonics Research, Silicon and Nanophotonics}, volume = {IPRSN}, booktitle = {Integrated Photonics Research, Silicon and Nanophotonics}, doi = {10.1364/IPRSN.2014.IW1A.3}, pages = {IW1A.3}, language = {en} } @article{GschreyThomaSchnauberetal., author = {Gschrey, Manuel and Thoma, Alexander and Schnauber, Peter and Seifried, Marc and Schmidt, Ronny and Wohlfeil, Benjamin and Kr{\"u}ger, Luzy and Schulze, Jan-Hindrick and Heindel, Tobias and Burger, Sven and Schmidt, Frank and Strittmatter, Andre and Rodt, Sven and Reitzenstein, Stephan}, title = {Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography}, series = {Nature Communications}, volume = {6}, journal = {Nature Communications}, doi = {10.1038/ncomms8662}, pages = {7662}, language = {en} } @inproceedings{ThomaSchnauberGschreyetal., author = {Thoma, Alexander and Schnauber, Peter and Gschrey, Manuel and Schmidt, Ronny and Wohlfeil, Benjamin and Seifried, Marc and Schulze, Jan-Hindrick and Burger, Sven and Schmidt, Frank and Strittmatter, Andre and Rodt, Sven and Heindel, Tobias and Reitzenstein, Stephan}, title = {Indistinguishable Photons from Deterministically Fabricated Quantum Dot Microlenses}, series = {Advanced Photonics}, booktitle = {Advanced Photonics}, doi = {10.1364/IPRSN.2015.IS4A.6}, pages = {IS4A.6}, language = {en} } @inproceedings{ScholzeLaubisDerschetal.2007, author = {Scholze, Frank and Laubis, Christian and Dersch, Uwe and Pomplun, Jan and Burger, Sven and Schmidt, Frank}, title = {The influence of line edge roughness and CD uniformity on EUV scatterometry for CD characterization of EUV masks}, series = {Modeling Aspects in Optical Metrology}, volume = {6617}, booktitle = {Modeling Aspects in Optical Metrology}, editor = {Bosse, Harald}, publisher = {Proc. SPIE}, pages = {66171A}, year = {2007}, language = {en} } @inproceedings{ScholzeLaubisUlmetal.2008, author = {Scholze, Frank and Laubis, Christian and Ulm, Gerhard and Dersch, Uwe and Pomplun, Jan and Burger, Sven and Schmidt, Frank}, title = {Evaluation of EUV scatterometry for CD characterization of EUV masks using rigorous FEM-simulation}, series = {Emerging Lithographic Technologies XII}, volume = {6921}, booktitle = {Emerging Lithographic Technologies XII}, editor = {Schellenberg, Frank}, publisher = {SPIE}, year = {2008}, language = {en} } @inproceedings{PomplunBurgerSchmidtetal.2008, author = {Pomplun, Jan and Burger, Sven and Schmidt, Frank and Scholze, Frank and Laubis, Christian and Dersch, Uwe}, title = {Metrology of EUV masks by EUV-scatterometry and finite element analysis}, series = {Photomask and Next-Generation Lithography Mask Technology XV}, volume = {7028}, booktitle = {Photomask and Next-Generation Lithography Mask Technology XV}, editor = {Horiuchi, Toshiyuki}, publisher = {SPIE}, year = {2008}, language = {en} } @inproceedings{PomplunBurgerSchmidtetal.2006, author = {Pomplun, Jan and Burger, Sven and Schmidt, Frank and Zschiedrich, Lin and Scholze, Frank}, title = {Rigorous FEM-Simulation of EUV-Masks: Influence of shape and material parameters}, series = {Photomask Technology}, volume = {6349}, booktitle = {Photomask Technology}, editor = {Martin, P. and Naber, R.}, publisher = {Proc. SPIE}, doi = {10.1117/12.686828}, pages = {63493D}, year = {2006}, language = {en} } @inproceedings{PomplunBurgerSchmidtetal.2007, author = {Pomplun, Jan and Burger, Sven and Schmidt, Frank and Scholze, Frank and Laubis, Christian and Dersch, Uwe}, title = {Finite element analysis of EUV lithography}, series = {Modeling Aspects in Optical Metrology}, volume = {6617}, booktitle = {Modeling Aspects in Optical Metrology}, editor = {Bosse, Harald}, publisher = {Proc. SPIE}, doi = {10.1117/12.726156}, pages = {661718}, year = {2007}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2011, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank and Kato, Akiko and Laubis, Christian and Scholze, Frank}, title = {Investigation of 3D Patterns on EUV Masks by Means of Scatterometry and Comparison to Numerical Simulations}, series = {Photomask Technology 2011}, volume = {8166}, booktitle = {Photomask Technology 2011}, publisher = {Proc. SPIE}, doi = {10.1117/12.896839}, pages = {81661Q}, year = {2011}, language = {en} } @misc{YevickFrieseSchmidt, author = {Yevick, David and Friese, Tilmann and Schmidt, Frank}, title = {A Comparison of Transparent Boundary Conditions for the Fresnel Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5738}, number = {00-05}, abstract = {We establish the relationship between the transparent boundary condition (BPP) of Baskakov and Popov [Wave Motion 14 (1991) 121-128] and Pakpadakis et. al. [J. Acoust. Soc. Am. 92 (1992) 2030-2038] and a second boundary condition (SDY) introduced by Schmidt and Deuflhard [Comp. Math. Appl. 29 (1995) 53-76] and Schmidt and Yevick [J. Compu. Phys. 134 (1997) 96-107], that is explicitly tailored to the form of the underlying numerical propagation scheme. Our analysis demonstrates that if the domain is first discretized in the propagation direction, the SDY expression can be obtained by applying the exact sequence of steps used to derive the BPP procedure. The BPP method is thus an approximate realization of the computationally far simpler and unconditionally stable SDY boundary condition.}, language = {en} } @misc{Schmidt, author = {Schmidt, Frank}, title = {Discrete Nonreflecting Boundary Conditions for the Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5744}, number = {00-06}, abstract = {We derive exact discrete nonreflecting boundary conditions for time-harmonic scattering problems modeled by the Helmholtz equation. The main idea is to consider the exterior problem as an initial value problem with initial data given on the boundary of the computational domain. The solution of the exterior problem is obtained via Laplace transformation techniques which supply the boundary conditions in terms of discrete Dirichlet-to-Neumann operators.}, language = {en} } @misc{HohageSchmidt, author = {Hohage, Thorsten and Schmidt, Frank}, title = {On the Numerical Solution of Nonlinear Schr{\"o}dinger type equations in fiber optics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6715}, number = {02-04}, abstract = {The aim of this paper is to develop fast methods for the solution of nonlinear Schr{\"o}dinger type equations in fiber optics. Using the method of lines we have to solve a stiff system of ordinary differential equations where the eigenvalues of the Jacobian are close to the imaginary axis. This is usually done by a Split Step method. Here we consider the extrapolation of Split Step methods with adaptive order and step size control. For more complicated nonlinearities, in particular stimulated Raman scattering, Split Step methods are less efficient since symmetry is either destroyed or requires much additional effort. In this case we use implicit Runge Kutta formulas of Gauß type. The key point for the efficient implementation of these methods is that the system of nonlinear algebraic equations can be solved without setting up the Jacobian. The proposed methods are compared to other methods, in particular exponential integrators, the method of Marcuse, and the method of Blow and Wood.}, language = {en} } @misc{CordesWeberSchmidtEhrenberg, author = {Cordes, Frank and Weber, Marcus and Schmidt-Ehrenberg, Johannes}, title = {Metastable Conformations via successive Perron-Cluster Cluster Analysis of dihedrals}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7074}, number = {02-40}, abstract = {Decomposition of the high dimensional conformational space of bio-molecules into metastable subsets is used for data reduction of long molecular trajectories in order to facilitate chemical analysis and to improve convergence of simulations within these subsets. The metastability is identified by the Perron-cluster cluster analysis of a Markov process that generates the thermodynamic distribution. A necessary prerequisite of this analysis is the discretization of the conformational space. A combinatorial approach via discretization of each degree of freedom will end in the so called ''curse of dimension''. In the following paper we analyze Hybrid Monte Carlo simulations of small, drug-like biomolecules and focus on the dihedral degrees of freedom as indicators of conformational changes. To avoid the ''curse of dimension'', the projection of the underlying Markov operator on each dihedral is analyzed according to its metastability. In each decomposition step of a recursive procedure, those significant dihedrals, which indicate high metastability, are used for further decomposition. The procedure is introduced as part of a hierarchical protocol of simulations at different temperatures. The convergence of simulations within metastable subsets is used as an ''a posteriori'' criterion for a successful identification of metastability. All results are presented with the visualization program AmiraMol.}, language = {en} } @misc{HohageSchmidtZschiedrich, author = {Hohage, Thorsten and Schmidt, Frank and Zschiedrich, Lin}, title = {Solving time-harmonic scattering problems based on the pole condition: Convergence of the PML method}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6494}, number = {01-23}, abstract = {In this paper we study the PML method for Helmholtz-type scattering problems with radially symmetric potential. The PML method consists in surrounding the computational domain by a \textbf{P}erfectly \textbf{M}atched sponge \textbf{L}ayer. We prove that the approximate solution obtained by the PML method converges exponentially fast to the true solution in the computational domain as the thickness of the sponge layer tends to infinity. This is a generalization of results by Lassas and Somersalo based on boundary integral eqaution techniques. Here we use techniques based on the pole condition instead. This makes it possible to treat problems without an explicitly known fundamental solution.}, language = {en} } @misc{HohageSchmidtZschiedrich, author = {Hohage, Thorsten and Schmidt, Frank and Zschiedrich, Lin}, title = {A new method for the solution of scattering problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6683}, number = {02-01}, abstract = {We present a new efficient algorithm for the solution of direct time-harmonic scattering problems based on the Laplace transform. This method does not rely on an explicit knowledge of a Green function or a series representation of the solution, and it can be used for the solution of problems with radially symmetric potentials and problems with waveguides. The starting point is an alternative characterization of outgoing waves called \emph{pole condition}, which is equivalent to Sommerfeld's radiation condition for problems with radially symmetric potentials. We obtain a new representation formula, which can be used for a numerical evaluation of the exterior field in a postprocessing step. Based on previous theoretical studies, we discuss the numerical realization of our algorithm and compare its performance to the PML method.}, language = {en} } @phdthesis{Schmidt, author = {Schmidt, Frank}, title = {A New Approach to Coupled Interior-Exterior Helmholtz-Type Problems: Theory and Algorithms}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7128}, number = {02-45}, abstract = {The work presents a new approach to the numerical solution of time-harmonic and time-dependent scattering problems. We replace Sommerfeld's radiation condition valid for the Helmholtz equation by a more general concept called pole condition. The pole condition is based on the Laplace transform of the exterior solution and allows a characterization of outgoing waves. Both new insight into the analysis of scattering problems as well as new numerical algorithms are obtained.}, language = {en} } @misc{ZschiedrichKloseSchaedleetal., author = {Zschiedrich, Lin and Klose, Roland and Sch{\"a}dle, Achim and Schmidt, Frank}, title = {A new Finite Element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2D}, doi = {10.1016/j.cam.2005.03.047}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7662}, number = {03-44}, abstract = {In this paper we propose a new finite element realization of the Perfectly Matched Layer method (PML-method). Our approach allows to deal with arbitrary shaped polygonal domains and with certain types of inhomogeneous exterior domains. Among the covered inhomogeneities are open waveguide structures playing an essential role in integrated optics. We give a detailed insight to implementation aspects. Numerical examples show exponential convergence behavior to the exact solution with the thickness of the PML sponge layer.}, language = {en} } @misc{MayEisenhardtSchmidtEhrenbergetal., author = {May, Andreas and Eisenhardt, Steffen and Schmidt-Ehrenberg, Johannes and Cordes, Frank}, title = {Rigid body docking for Virtual Screening}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7690}, number = {03-47}, abstract = {A recently developed algorithm allows Rigid Body Docking of ligands to proteins, regardless of the accessibility and location of the binding site. The Docking procedure is divided into three subsequent optimization phases, two of which utilize rigid body dynamics. The last one is applied with the ligand already positioned inside the binding pocket and accounts for full flexibility. Initially, a combination of geometrical and force-field based methods is used as a Coarse Docking strategy, considering only Lennard-Jones interactions between the target and pharmaceutically relevant atoms or functional groups. The protein is subjected to a Hot Spot Analysis, which reveals points of high affinity in the protein environment towards these groups. The hot spots are distributed into different subsets according to their group affiliation. The ligand is described as a complementary point set, consisting of the same subsets. Both sets are matched in \$\mathrm{I\!R}^{3}\$, by superimposing members of the same subsets. In the first instance, steric inhibition is nearly neglected, preventing the system's trajectory from trapping in local minima and thus from finding false positive solutions. Hence the exact location of the binding site can be determined fast and reliably without any additional information. Subsequently, errors resulting from approximations are minimized via finetuning, this time considering both Lennard-Jones and Coulomb forces. Finally, the potential energy of the whole complex is minimized. In a first evaluation, results are rated by a reduced scoring function considering only noncovalent interaction energies. Exemplary Screening results will be given for specific ligands.}, language = {en} } @misc{RuprechtSchaedleSchmidtetal., author = {Ruprecht, Daniel and Sch{\"a}dle, Achim and Schmidt, Frank and Zschiedrich, Lin}, title = {Transparent boundary conditons for time-dependent problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9558}, number = {07-12}, abstract = {A new approach to derive transparent boundary conditions (TBCs) for wave, Schr{\"o}dinger, heat and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physical reasonable and unreasonable solutions by the location of the singularities of the spatial Laplace transform of the exterior solution. To obtain a numerical algorithm, a M{\"o}bius transform is applied to map the Laplace transform onto the unit disc. In the transformed coordinate the solution is expanded into a power series. Finally, equations for the coefficients of the power series are derived. These are coupled to the equation in the interior, and yield transparent boundary conditions. Numerical results are presented in the last section, showing that the error introduced by the new approximate TBCs decays exponentially in the number of coefficients.}, language = {en} } @misc{SchaedleZschiedrichBurgeretal., author = {Sch{\"a}dle, Achim and Zschiedrich, Lin and Burger, Sven and Klose, Roland and Schmidt, Frank}, title = {Domain Decomposition Method for Maxwell's Equations: Scattering off Periodic Structures}, doi = {/10.1016/j.jcp.2007.04.017}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8984}, number = {06-04}, abstract = {We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). To cope with Wood anomalies appearing in periodic structures an adaptive strategy to determine optimal PML parameters is developed. We focus on the application to typical EUV lithography line masks. Light propagation within the multi-layer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer.}, language = {en} } @misc{DeuflhardFrieseSchmidtetal., author = {Deuflhard, Peter and Friese, Tilmann and Schmidt, Frank and M{\"a}rz, Reinhard and Nolting, Hans-Peter}, title = {Effiziente Eigenmodenberechnung f{\"u}r den Entwurf integriert-optischer Chips}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2131}, number = {SC-96-02}, abstract = {{\bf Efficient eigenmode computation for the design of integrated optical chips.}The paper deals with adaptive multigrid methods for 2D Helmholtz eigenvalue problems arising in the design of integrated optical chips. Typical features of the technological problem are its geometric complexity, its multiscale structure, the possible occurrence of eigenvalue clusters, and the necessity of quite stringent required relative error tolerances. For reasons of sheer computational complexity, multigrid methods must be used to solve the discretized eigenvalue problems and adaptive grids must be automatically constructed to avoid an undesirable blow-up of the required number of nodes for these accuracies. In view of the problem specifications, an adaptive multigrid method based on Rayleigh quotient minimization, simultaneous eigenspace iteration, and conjugate gradient method as smoother is carefully selected. Its performance in the numerical simulation of a component of a rather recent optical chip (heterodyne receiver of HHI) is documented.}, language = {de} } @misc{Schmidt, author = {Schmidt, Frank}, title = {Simultaneous Computation of the Lowest Eigenvalue and Eigenvectors of the Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5281}, number = {TR-95-13}, abstract = {This report collects a number of proposals to determine the lowest eigensolutions of the scalar Helmholtz equation. The basic routine of all discussed algorithms is the standard Rayleigh quotient minimization process. The minimization is performed in a direct multilevel manner, and a subspace iteration is used to determine simultaneously a couple of eigensolutions. As smoother the nonlinear Gauß-Seidel, the nonlinear conjugate gradient method and a preconditioned version of this method are compared with respect to their efficiency. The numerical examples are based on realistic 1D and 2D models of integrated optics components.}, language = {en} } @misc{FrieseSchmidtYevick, author = {Friese, Tilman and Schmidt, Frank and Yevick, David}, title = {Transparent Boundary Conditions for a Wide-Angle Approximation of the One-Way Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4345}, number = {SC-99-45}, abstract = {We present nonlocal discrete transparent boundary conditions for a fourth-order wide-angle approximation of the two-dimensional Helmholtz equation. The boundary conditions are exact in the sense that they supply the same discrete solution on a bounded interior domain as would be obtained by considering the problem on the entire unbounded domain with zero boundary conditions at infinity. The proposed algorithm results in an unconditionally stable propagation method. Numerical examples from optics illustrate the efficiency of our approach.}, language = {en} } @misc{SchmidtFrieseYevick, author = {Schmidt, Frank and Friese, Tilmann and Yevick, David}, title = {Transparent Boundary Conditions for Split-Step Pade Approximations of the One-Way Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4353}, number = {SC-99-46}, abstract = {In this paper, we generalize the nonlocal discrete transparent boundary condition introduced by Schmidt and Deuflhard {[}Comp. Math. Appl. 29 (1995) 53-76{]} and Schmidt and Yevick {[}J. Comput. Phys. 134 (1997) 96-107{]} to propagation methods based on arbitrary Pad\'e approximations to the two-dimensional one-way Helmholtz equation. Our approach leads to a recursive formula for the coefficients appearing in the nonlocal condition which then yields an unconditionally stable propagation method.}, language = {en} } @misc{Schmidt, author = {Schmidt, Frank}, title = {An Alternative Derivation of the Exact DtN-Map on a Circle}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3752}, number = {SC-98-32}, abstract = {The paper supplies an alternative derivation of the exact boundary conditions needed for the solution of time-harmonic acoustic scattering problems modeled by the Helmholtz equation. The main idea is to consider the exterior domain problem as an initial value problem with initial data given on the boundary of a disc or sphere. The solution of the exterior domain problem is obtained via Laplace transformation techniques, where the asymptotic Sommerfeld radiation condition is reformulated accordingly.}, language = {en} } @misc{Schmidt, author = {Schmidt, Frank}, title = {An Adaptive Approach to the Numerical Solution of Fresnel's Wave Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-628}, number = {SC-91-12}, abstract = {An adaptive approach to the numerical solution of the wave propagation in integrated optics devices with 1D cross sections is described. First, Fresnel's approximation of the exact wave equation resulting from Maxwell's equations is considered. A criterion to estimate the validity of this approximation is derived. Fresnel's wave equation being formally equivalent to Schroedinger's equation uniquely defines an initial-boundary-value problem, which is solved numerically by a stepwise calculation of the propagating field. Discretization in longitudinal direction first with stepsize control leads to a stationary subproblem for the transversal field distribution, which is then handled by an adaptive finite element method. Thus full adaptivity of the algorithm is realized. The numerical examples are concentrated on taper structures playing an essential role in integrated optics devices for telecommunication systems.}, language = {en} } @misc{SchmidtMaerz, author = {Schmidt, Frank and M{\"a}rz, Reinhard}, title = {On the Reference Wave Vector pf Paraxial Helmholtz Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1660}, number = {SC-94-38}, abstract = {The reference wave vector of the paraxial Helmholtz equation is determined using various strategies which result all in similar expressions. The effort for its evaluation is so small that the reference wave vector can be adapted for each propagation step of an arbitrary BPM-algorithm.}, language = {en} } @misc{DeuflhardSchmidt, author = {Deuflhard, Peter and Schmidt, Frank}, title = {Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel's Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1205}, number = {SC-93-24}, abstract = {The paper presents a construction scheme of deriving transparent , i. e. reflection-free, boundary conditions for the numerical solution of Fresnel's equation (being formally equivalent to Schr{\"o}dinger's equation). These boundary conditions appear to be of a nonlocal Cauchy type. As it turns out, each kind of linear implicit discretization induces its own discrete transparent boundary conditions.}, language = {en} } @misc{Schmidt, author = {Schmidt, Frank}, title = {Computation of Discrete Transparent Boundary Conditions for the 2D Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3330}, number = {SC-97-64}, abstract = {We present a family of nonlocal transparent boundary conditions for the 2D Helmholtz equation. The whole domain, on which the Helmholtz equation is defined, is decomposed into an interior and an exterior domain. The corresponding interior Helmholtz problem is formulated as a variational problem in standard manner, representing a boundary value problem, whereas the exterior problem is posed as an initial value problem in the radial variable. This problem is then solved approximately by means of the Laplace transformation. The derived boundary conditions are asymptotically correct, model inhomogeneous exterior domains and are simple to implement.}, language = {en} } @misc{SchmidtYevick, author = {Schmidt, Frank and Yevick, David}, title = {Discrete Transparent Boundary Conditions for Schr{\"o}dinger-Type Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2289}, number = {SC-96-17}, abstract = {We present a general technique for constructing nonlocal transparent boundary conditions for one-dimensional Schr{\"o}dinger-type equations. Our method supplies boundary conditions for the \$\theta\$-family of implicit one-step discretizations of Schr{\"o}dinger's equation in time. The use of Mikusi\'nski's operator approach in time avoids direct and inverse transforms between time and frequency domains and thus implements the boundary conditions in a direct manner.}, language = {en} } @misc{DeuflhardFrieseSchmidt, author = {Deuflhard, Peter and Friese, Tilmann and Schmidt, Frank}, title = {A Nonlinear Multigrid Eigenproblem Solver for the Complex Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3240}, number = {SC-97-55}, abstract = {The paper is motivated by the need for a fast robust adaptive multigrid method to solve complex Helmholtz eigenvalue problems arising from the design of optical chips. A nonlinear multigrid method is developed, which can be regarded as an extension of a previous adaptive Rayleigh quotient minimization method for selfadjoint Helmholtz eigenproblems. Since the complex Helmholtz operator is just a compact nonselfadjoint perturbation of a selfadjoint operator, linear algebra techniques like Schur decomposition can be extended from the finite dimensional case. The efficiency of the derived adaptive nonlinear multigrid method is illustrated by computations for a technologically relevant integrated optics component containing Multi Quantum Well Layers.}, language = {en} } @misc{Schmidt, author = {Schmidt, Frank}, title = {Construction of Discrete Transparent Boundary Conditions for Schr{\"o}dinger-Type Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3292}, number = {SC-97-60}, abstract = {We present a general technique for constructing nonlocal transparent boundary conditions for time-discretized one-dimensional Schr{\"o}dinger type equations. The main tool of construction is the discrete counterpart to Mikusi\'nski's continuous algebraic operator approach. Existing techniques are simplified and generalized. Both adaptive time-steps and time-dependent exterior potentials are taken into account.}, language = {en} } @misc{SchmidtFrieseZschiedrichetal., author = {Schmidt, Frank and Friese, Tilmann and Zschiedrich, Lin and Deuflhard, Peter}, title = {Adaptive Multigrid Methods for the Vectorial Maxwell Eigenvalue Problem for Optical Waveguide Design}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6228}, number = {00-54}, abstract = {This paper has been motivated by the need for a fast robust adaptive multigrid method to solve the vectorial Maxwell eigenvalue problem arising from the design of optical chips. Our nonlinear multigrid methods are based on a previous method for the scalar Helmholtz equation, which must be modified to cope with the null space of the Maxwell operator due to the divergence condition. We present two different approaches. First, we present a multigrid algorithm based on an edge element discretization of time-harmonic Maxwell's equations, including the divergence condition. Second, an explicit elimination of longitudinal magnetic components leads to a nodal discretization known to avoid discrete \emph{spurious modes} also and a vectorial eigenvalue problem, for which we present a multigrid solver. Numerical examples show that the edge element discretization clearly outperforms the nodal element approach.}, language = {en} } @misc{HohageSchmidtZschiedrich, author = {Hohage, Thorsten and Schmidt, Frank and Zschiedrich, Lin}, title = {Solving time-harmonic scattering problems based on the condition: Theory}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6279}, number = {01-01}, abstract = {The pole condition is a general concept for the theoretical analysis and the numerical solution of a variety of wave propagation problems. It says that the Laplace transform of the physical solution in radial direction has no poles in the lower complex half-plane. In the present paper we show that for the Helmholtz equation with a radially symmetric potential the pole condition is equivalent to Sommerfeld's radiation condition. Moreover, a new representation formula based on the pole condition is derived and used to prove existence, uniqueness and asymptotic properties of solutions. This lays the foundations of a promising new algorithm to solve time-harmonic scattering problems numerically and provides a new approach for analyzing existing algorithms such as the Perfectly Matched Layer (PML) method and the Bayliss-Gunzburger-Turkel (BGT) algorithm.}, language = {en} } @article{BlomeMcPeakBurgeretal.2014, author = {Blome, Mark and McPeak, Kevin and Burger, Sven and Schmidt, Frank and Norris, David}, title = {Back-reflector design in thin-film silicon solar cells by rigorous 3D light propagation modeling}, series = {COMPEL: Int. J. Comput. Mathem. Electr. Electron. Eng.}, volume = {33}, journal = {COMPEL: Int. J. Comput. Mathem. Electr. Electron. Eng.}, number = {4}, doi = {10.1108/COMPEL-12-2012-0367}, pages = {1282 -- 1295}, year = {2014}, language = {en} } @incollection{BurgerKloseSchaedleetal.2006, author = {Burger, Sven and Klose, Roland and Sch{\"a}dle, Achim and Schmidt, Frank and Zschiedrich, Lin}, title = {Adaptive FEM solver for the computation of electromagnetic eigenmodes in 3D photonic crystal structures}, series = {Scientific Computing in Electrical Engineering}, booktitle = {Scientific Computing in Electrical Engineering}, publisher = {Springer Verlag}, doi = {10.1007/978-3-540-32862-9_24}, pages = {169 -- 175}, year = {2006}, language = {en} } @inproceedings{BurgerKleemannZschiedrichetal.2009, author = {Burger, Sven and Kleemann, B. and Zschiedrich, Lin and Schmidt, Frank}, title = {Finite-Element Simulations of Light Propagation through Circular Subwavelength Apertures}, series = {Microtechnologies for the New Millenium}, volume = {7366}, booktitle = {Microtechnologies for the New Millenium}, publisher = {Proc. SPIE}, doi = {10.1117/12.822828}, pages = {736621}, year = {2009}, language = {en} } @inproceedings{BurgerKoehleZschiedrichetal.2006, author = {Burger, Sven and K{\"o}hle, Roderick and Zschiedrich, Lin and Nguyen, H. and Schmidt, Frank and M{\"a}rz, Reinhard and N{\"o}lscher, Christoph}, title = {Rigorous Simulation of 3D Masks}, series = {Photomask Technology}, volume = {6349}, booktitle = {Photomask Technology}, editor = {Martin, P. and Naber, R.}, publisher = {Proc. SPIE}, pages = {63494Z}, year = {2006}, language = {en} } @inproceedings{BurgerKoehleZschiedrichetal.2005, author = {Burger, Sven and K{\"o}hle, Roderick and Zschiedrich, Lin and Gao, W. and Schmidt, Frank and M{\"a}rz, Reinhard and N{\"o}lscher, Christoph}, title = {Benchmark of FEM, Waveguide and FDTD Algorithms for Rigorous Mask Simulation}, series = {Photomask Technology}, volume = {5992}, booktitle = {Photomask Technology}, editor = {Weed, J. and Martin, P.}, publisher = {Proc. SPIE}, doi = {10.1117/12.631696}, pages = {378 -- 389}, year = {2005}, language = {en} } @inproceedings{BurgerLockauZschiedrichetal.2009, author = {Burger, Sven and Lockau, D. and Zschiedrich, Lin and Schmidt, Frank}, title = {Finite-element simulations of light propagation through subwavelength apertures in metal films}, series = {International Workshop on Optical Waveguide Theory and Numerical Modelling}, volume = {XVIII}, booktitle = {International Workshop on Optical Waveguide Theory and Numerical Modelling}, publisher = {Fraunhofer Institute for Applied Optics and Precision Engineering}, pages = {59}, year = {2009}, language = {en} } @incollection{BurgerPomplunSchmidt2012, author = {Burger, Sven and Pomplun, Jan and Schmidt, Frank}, title = {Finite Element Methods for Computational Nano-optics}, series = {Encyclopedia of Nanotechnology}, booktitle = {Encyclopedia of Nanotechnology}, editor = {Bhushan, B.}, publisher = {Springer Netherlands}, doi = {10.1007/978-90-481-9751-4_17}, pages = {837 -- 843}, year = {2012}, language = {en} } @inproceedings{BurgerSchmidtZschiedrich2003, author = {Burger, Sven and Schmidt, Frank and Zschiedrich, Lin}, title = {A fast and efficient Finite-Element Solver for 2D and 3D Photonic Band-Gap Problems}, series = {Dig. LEOS/IEEE 2003 Summer Topicals}, booktitle = {Dig. LEOS/IEEE 2003 Summer Topicals}, doi = {10.1109/LEOSST.2003.1224282}, pages = {75}, year = {2003}, language = {en} } @inproceedings{BurgerZschiedrichSchmidt2010, author = {Burger, Sven and Zschiedrich, Lin and Schmidt, Frank}, title = {3D FEM Simulations of High-Q Resonances in Photonic Crystal Microcavities}, series = {Integrated Photonics Research, Silicon and Nanophotonics}, booktitle = {Integrated Photonics Research, Silicon and Nanophotonics}, publisher = {OSA}, doi = {10.1364/IPRSN.2010.IWB7}, pages = {IWB7}, year = {2010}, language = {en} } @inproceedings{BurgerSchmidtZschiedrich2010, author = {Burger, Sven and Schmidt, Frank and Zschiedrich, Lin}, title = {FEM simulation of resonances in low-Q cavities for plasmon lasers}, series = {International Workshop on Photonic Nanomaterials}, booktitle = {International Workshop on Photonic Nanomaterials}, editor = {Jena, Friedrich-Schiller-Universit{\"a}t}, isbn = {978-3-00-031358-5}, pages = {36}, year = {2010}, language = {en} } @inproceedings{BurgerSchmidtZschiedrich2010, author = {Burger, Sven and Schmidt, Frank and Zschiedrich, Lin}, title = {Numerical investigation of optical resonances in circular grating resonators}, series = {Silicon Photonics V}, volume = {7606}, booktitle = {Silicon Photonics V}, publisher = {Proc. SPIE}, doi = {10.1117/12.842061}, pages = {760610}, year = {2010}, language = {en} } @inproceedings{BurgerSchmidtZschiedrich2010, author = {Burger, Sven and Schmidt, Frank and Zschiedrich, Lin}, title = {Numerical Investigation of Photonic Crystal Microcavities in Silicon-on-Insulator Waveguides}, series = {Photonic and Phononic Crystal Materials and Devices X}, volume = {7609}, booktitle = {Photonic and Phononic Crystal Materials and Devices X}, publisher = {Proc. SPIE}, doi = {10.1117/12.841867}, pages = {76091Q}, year = {2010}, language = {en} } @inproceedings{PomplunZschiedrichBurgeretal.2010, author = {Pomplun, Jan and Zschiedrich, Lin and Burger, Sven and Schmidt, Frank and Tyminski, Jacek and Flagello, Donis and Toshiharu, N.}, title = {Reduced basis method for source mask optimization}, series = {Photomask Technology}, volume = {7823}, booktitle = {Photomask Technology}, publisher = {Proc. SPIE}, doi = {10.1117/12.866101}, pages = {78230E}, year = {2010}, language = {en} } @inproceedings{BurgerSchaedleZschiedrichetal.2006, author = {Burger, Sven and Sch{\"a}dle, Achim and Zschiedrich, Lin and Schmidt, Frank}, title = {Advanced FEM Analysis of Nano-Optical Devices}, series = {Nanophotonics}, volume = {6195}, booktitle = {Nanophotonics}, editor = {Andrews, David L. and Nunzi, Jean-Michel and Ostendorf, Andreas}, publisher = {Proc. SPIE}, doi = {10.1117/12.662942}, pages = {72 -- 82}, year = {2006}, language = {en} } @incollection{BurgerZschiedrichKettneretal.2008, author = {Burger, Sven and Zschiedrich, Lin and Kettner, Benjamin and Schmidt, Frank}, title = {FEM simulation of light scattering by nonspherical objects}, series = {Mie Theory 1908 - 2008}, booktitle = {Mie Theory 1908 - 2008}, editor = {Hergert, W. and Wriedt, T.}, publisher = {Universit{\"a}t Bremen}, pages = {82 -- 83}, year = {2008}, language = {en} } @inproceedings{BurgerZschiedrichKloseetal.2005, author = {Burger, Sven and Zschiedrich, Lin and Klose, Roland and Sch{\"a}dle, Achim and Schmidt, Frank and Enkrich, Christian and Linden, S. and Wegener, M. and Soukoulis, C.}, title = {Numerical Investigation of Light Scattering off Split-Ring Resonators}, series = {Metamaterials}, volume = {5955}, booktitle = {Metamaterials}, editor = {Szoplik, T. and {\"O}zbay, E. and Soukoulis, C. and Zheludev, N.}, publisher = {Proc. SPIE}, doi = {10.1117/12.622184}, pages = {18 -- 26}, year = {2005}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2009, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank and Kettner, Benjamin and Lockau, D.}, title = {3D Finite-Element Simulations of Enhanced Light Transmission Through Arrays of Holes in Metal Films}, series = {Numerical Methods in Optical Metrology}, volume = {7390}, booktitle = {Numerical Methods in Optical Metrology}, publisher = {Proc. SPIE}, doi = {10.1117/12.827543}, pages = {73900H}, year = {2009}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2010, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank}, title = {Finite element method for accurate 3D simulation of plasmonic waveguides}, series = {Integrated Optics: Devices, Materials, and Technologies XIV}, volume = {7604}, booktitle = {Integrated Optics: Devices, Materials, and Technologies XIV}, publisher = {Proc. SPIE}, doi = {10.1117/12.841995}, pages = {76040F}, year = {2010}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2008, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank}, title = {JCMsuite: An Adaptive FEM Solver for Precise Simulations in Nano-Optics}, series = {Integrated Photonics and Nanophotonics Research and Applications}, booktitle = {Integrated Photonics and Nanophotonics Research and Applications}, publisher = {Optical Society of America}, doi = {10.1364/IPNRA.2008.ITuE4}, pages = {ITuE4}, year = {2008}, language = {en} } @article{BurgerZschiedrichSchmidt2010, author = {Burger, Sven and Zschiedrich, Lin and Schmidt, Frank}, title = {FEM Simulation of Plasmon Laser Resonances}, series = {AIP Conference Proceedings}, volume = {1281}, journal = {AIP Conference Proceedings}, publisher = {AIP}, doi = {10.1063/1.3498131}, pages = {1613 -- 1616}, year = {2010}, language = {en} } @inproceedings{BurgerKloseMaerzetal.2004, author = {Burger, Sven and Klose, Roland and M{\"a}rz, Reinhard and Sch{\"a}dle, Achim and Schmidt, Frank and Zschiedrich, Lin}, title = {Efficient Finite Element Methods for the Design of Microoptical Components}, series = {Proc. Microoptics Conf. 2004}, booktitle = {Proc. Microoptics Conf. 2004}, year = {2004}, language = {en} } @inproceedings{BurgerKloseSchaedleetal.2005, author = {Burger, Sven and Klose, Roland and Sch{\"a}dle, Achim and Schmidt, Frank and Zschiedrich, Lin}, title = {FEM modelling of 3D photonic crystals and photonic crystal waveguides}, series = {Integrated Optics : Devices, Materials and Technologies IX}, volume = {5728}, booktitle = {Integrated Optics : Devices, Materials and Technologies IX}, editor = {Sidorin, Y. and W{\"a}chter, Christoph}, publisher = {Proc. SPIE}, doi = {10.1117/12.585895}, pages = {164 -- 173}, year = {2005}, language = {en} } @article{SchmidtFrieseYevick2001, author = {Schmidt, Frank and Friese, T. and Yevick, David}, title = {Transparent Boundary Conditions for Split-Step Pad{\´e} Approximations of the One-Way Helmholtz equation}, series = {J. Comp. Phys}, volume = {170}, journal = {J. Comp. Phys}, pages = {696 -- 719}, year = {2001}, language = {en} } @incollection{SchmidtFrieseZschiedrichetal.2003, author = {Schmidt, Frank and Friese, T. and Zschiedrich, Lin and Deuflhard, Peter}, title = {Adaptive Multigrid Methods for the Vectorial Maxwell Eigenvalue Problem for Optical Waveguide Design}, series = {Mathematics - Key Technology for the Future}, booktitle = {Mathematics - Key Technology for the Future}, publisher = {Springer}, pages = {270 -- 292}, year = {2003}, language = {en} } @article{SchmidtGottschling1992, author = {Schmidt, Frank and Gottschling, K.}, title = {Improved Method of Mode Determination in Planar Optical Waveguides Using Line Transmission Approach}, series = {J. Opt. Commun.}, volume = {12}, journal = {J. Opt. Commun.}, number = {3}, pages = {112 -- 114}, year = {1992}, language = {en} } @article{SchmidtHohageKloseetal.2008, author = {Schmidt, Frank and Hohage, Thorsten and Klose, Roland and Sch{\"a}dle, Achim and Zschiedrich, Lin}, title = {Pole condition: A numerical method for Helmholtz-type scattering problems with inhomogeneous exterior domain}, series = {J. Comput. Appl. Math.}, volume = {218}, journal = {J. Comput. Appl. Math.}, number = {1}, doi = {10.1016/j.cam.2007.04.046}, pages = {61 -- 69}, year = {2008}, language = {en} } @article{SchmidtMaerz1996, author = {Schmidt, Frank and M{\"a}rz, Reinhard}, title = {On the Reference Wave Vector of Paraxial Helmholtz Equations}, series = {IEEE Journal of Lightwave Technology}, volume = {14}, journal = {IEEE Journal of Lightwave Technology}, pages = {2395 -- 2400}, year = {1996}, language = {en} } @article{PomplunSchmidt2010, author = {Pomplun, Jan and Schmidt, Frank}, title = {Accelerated a posteriori error estimation for the reduced basis method with application to 3D electromagnetic scattering problems}, series = {SIAM J. Sci. Comput.}, volume = {32}, journal = {SIAM J. Sci. Comput.}, doi = {10.1137/090760271}, pages = {498 -- 520}, year = {2010}, language = {en} } @inproceedings{PomplunSchmidt2009, author = {Pomplun, Jan and Schmidt, Frank}, title = {Reduced basis method for fast and robust simulation of electromagnetic scattering problems}, series = {Numerical Methods in Optical Metrology}, volume = {7390}, booktitle = {Numerical Methods in Optical Metrology}, publisher = {Proc. SPIE}, doi = {10.1117/12.827588}, pages = {73900I}, year = {2009}, language = {en} } @inproceedings{PomplunZschiedrichBurgeretal.2009, author = {Pomplun, Jan and Zschiedrich, Lin and Burger, Sven and Schmidt, Frank}, title = {Reduced basis method for computational lithography}, series = {Photomask Technology}, volume = {7488}, booktitle = {Photomask Technology}, publisher = {Proc. SPIE}, doi = {10.1117/12.829639}, pages = {74882B}, year = {2009}, language = {en} } @inproceedings{PhilippowSchmidt1987, author = {Philippow, E. and Schmidt, Frank}, title = {Besondere L{\"o}sungen in harmonisch erregten Ferroresonanz-Kreisen}, series = {4. Internationales Symposium Theoretische Elektrotechnik Ilmenau}, volume = {2}, booktitle = {4. Internationales Symposium Theoretische Elektrotechnik Ilmenau}, pages = {26 -- 32}, year = {1987}, language = {en} } @inproceedings{SchmidtBurgerPomplunetal.2008, author = {Schmidt, Frank and Burger, Sven and Pomplun, Jan and Zschiedrich, Lin}, title = {Advanced FEM analysis of optical waveguides: algorithms and applications}, series = {Integrated Optics}, volume = {6896}, booktitle = {Integrated Optics}, editor = {Greiner, Christoph and W{\"a}chter, Christoph}, publisher = {SPIE}, doi = {10.1117/12.765720}, pages = {689602}, year = {2008}, language = {en} } @inproceedings{SchmidtBurgerSchaedleetal.2005, author = {Schmidt, Frank and Burger, Sven and Sch{\"a}dle, Achim and Klose, Roland}, title = {Finite element methods for optical device design}, series = {Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic devices}, booktitle = {Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic devices}, doi = {10.1109/NUSOD.2005.1518133}, pages = {57 -- 58}, year = {2005}, language = {en} } @inproceedings{SchmidtDeuflhard1994, author = {Schmidt, Frank and Deuflhard, Peter}, title = {Discrete Transparent Boundary Conditions for Fresnel's Equation}, series = {Integrated Photonics Research}, booktitle = {Integrated Photonics Research}, address = {San Francisco, California, USA}, pages = {45 -- 47}, year = {1994}, language = {en} } @article{SchmidtDeuflhard1995, author = {Schmidt, Frank and Deuflhard, Peter}, title = {Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel's Equation.}, series = {Comput. Math. Appl.}, volume = {29}, journal = {Comput. Math. Appl.}, pages = {53 -- 76}, year = {1995}, language = {en} } @inproceedings{Schmidt2000, author = {Schmidt, Frank}, title = {Discrete Nonreflecting Boundary Conditions for the Helmholtz equation}, series = {Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation}, booktitle = {Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation}, editor = {Berm{\´u}dez, A. and G{\´o}mez, D. and Hazard, C. and Joly, P. and Roberts, J.}, address = {Waves 2000, Santiago de Compostella, Spain}, pages = {921 -- 925}, year = {2000}, language = {en} } @article{PomplunBurgerSchmidtetal.2010, author = {Pomplun, Jan and Burger, Sven and Schmidt, Frank and Schliwa, Andrei and Bimberg, Dieter and Pietrzak, Agnieszka and Wenzel, Hans and Erbert, G{\"o}tz}, title = {Finite element simulation of the optical modes of semiconductor lasers}, series = {Phys. Status Solidi B}, volume = {247}, journal = {Phys. Status Solidi B}, doi = {10.1002/pssb.200945451}, pages = {846 -- 853}, year = {2010}, language = {en} } @article{PomplunBurgerZschiedrichetal.2007, author = {Pomplun, Jan and Burger, Sven and Zschiedrich, Lin and Schmidt, Frank}, title = {Adaptive finite element method for simulation of optical nano structures}, series = {Phys. Status Solidi B}, volume = {244}, journal = {Phys. Status Solidi B}, doi = {10.1002/pssb.200743192}, pages = {3419 -- 3434}, year = {2007}, language = {en} } @inproceedings{PomplunHolzloehnerBurgeretal.2007, author = {Pomplun, Jan and Holzl{\"o}hner, Ronald and Burger, Sven and Zschiedrich, Lin and Schmidt, Frank}, title = {FEM investigation of leaky modes in hollow core photonic crystal fibers}, series = {Proc. SPIE, Photonic Crystal Materials and Devices VI}, volume = {6480}, booktitle = {Proc. SPIE, Photonic Crystal Materials and Devices VI}, editor = {Adibi, Ali and Scherer, Axel and Lin, Shawn-Yu}, pages = {64800M}, year = {2007}, language = {en} } @incollection{PomplunSchmidt2010, author = {Pomplun, Jan and Schmidt, Frank}, title = {Reduced Basis Method for Electromagnetic Field Computations}, series = {Scientific Computing in Electrical Engineering SCEE 2008}, booktitle = {Scientific Computing in Electrical Engineering SCEE 2008}, publisher = {Springer Berlin Heidelberg}, doi = {10.1007/978-3-642-12294-1_12}, pages = {85}, year = {2010}, language = {en} } @inproceedings{PomplunSchmidt2008, author = {Pomplun, Jan and Schmidt, Frank}, title = {Reduced Basis Method for Nano Optical Simulations}, series = {Integrated Photonics and Nanophotonics Research and Applications}, booktitle = {Integrated Photonics and Nanophotonics Research and Applications}, publisher = {Optical Society of America}, pages = {IWD7}, year = {2008}, language = {en} } @inproceedings{PomplunSchmidtBurgeretal.2010, author = {Pomplun, Jan and Schmidt, Frank and Burger, Sven and Zschiedrich, Lin}, title = {Adaptive Reduced Basis Method for Optical Scattering Problems}, series = {Integrated Photonics Research, Silicon and Nanophotonics}, booktitle = {Integrated Photonics Research, Silicon and Nanophotonics}, publisher = {OSA}, doi = {10.1364/IPRSN.2010.IWD4}, pages = {IWD4}, year = {2010}, language = {en} } @article{PomplunZschiedrichKloseetal.2007, author = {Pomplun, Jan and Zschiedrich, Lin and Klose, Roland and Schmidt, Frank and Burger, Sven}, title = {Finite element simulation of radiation losses in photonic crystal fibers}, series = {phys. stat. sol. (a)}, volume = {204}, journal = {phys. stat. sol. (a)}, number = {11}, doi = {10.1002/pssa.200776414}, pages = {3822 -- 3837}, year = {2007}, language = {en} } @inproceedings{PomplunBurgerZschiedrichetal.2011, author = {Pomplun, Jan and Burger, Sven and Zschiedrich, Lin and Schmidt, Frank}, title = {Reduced basis method for real-time inverse scatterometry}, series = {Modelling Aspects in Optical Metrology III}, volume = {8083}, booktitle = {Modelling Aspects in Optical Metrology III}, publisher = {Proc. SPIE}, doi = {10.1117/12.889892}, pages = {808308}, year = {2011}, language = {en} } @inproceedings{PomplunWenzelBurgeretal.2012, author = {Pomplun, Jan and Wenzel, Hans and Burger, Sven and Zschiedrich, Lin and Rozova, Maria and Schmidt, Frank and Crump, Paul and Ekhteraei, Hossein and Schultz, Christoph M. and Erbert, G{\"o}tz}, title = {Thermo-optical simulation of high-power diode lasers}, series = {Proc. SPIE}, volume = {8255}, booktitle = {Proc. SPIE}, doi = {10.1117/12.909330}, pages = {825510}, year = {2012}, language = {en} } @phdthesis{Schmidt2002, author = {Schmidt, Frank}, title = {Solution of Interior-Exterior Helmholtz-Type Problems Based on the Pole Condition Concept}, year = {2002}, language = {en} } @article{Schmidt2004, author = {Schmidt, Frank}, title = {Pole Condition: A new Approach to Solve Scattering Problems}, series = {Oberwolfach Report}, volume = {1}, journal = {Oberwolfach Report}, number = {1}, publisher = {Mathematisches Forschungsinstitut Oberwolfach}, pages = {615 -- 617}, year = {2004}, language = {en} } @phdthesis{Schmidt1989, author = {Schmidt, Frank}, title = {Ingenieurm{\"a}ßige Berechnung der Feldausbreitung in optischen Bauelementen der Lichtwellenleitertechnik}, year = {1989}, language = {en} } @article{Schmidt1990, author = {Schmidt, Frank}, title = {Simulation und Herstellung von Faserschleifkopplern}, series = {Wissenschaftliche Zeitschrift der Humboldt-Universit{\"a}t zu Berlin, R. Math./Naturwiss.}, volume = {39}, journal = {Wissenschaftliche Zeitschrift der Humboldt-Universit{\"a}t zu Berlin, R. Math./Naturwiss.}, number = {2}, pages = {115 -- 118}, year = {1990}, language = {en} } @article{Schmidt1993, author = {Schmidt, Frank}, title = {An Adaptive Approach to the Numerical Solution of Fresnel's Wave Equation.}, series = {IEEE Journal of Lightwave Technology}, volume = {11}, journal = {IEEE Journal of Lightwave Technology}, number = {9}, pages = {1425 -- 1435}, year = {1993}, language = {en} } @inproceedings{Schmidt1994, author = {Schmidt, Frank}, title = {Phase-adaptive basis functions for a multilevel finite element solution of the paraxial wave equation}, series = {Euro-Opto Series}, booktitle = {Euro-Opto Series}, editor = {G. C. Righini, D.}, address = {Lindau, Germany}, pages = {57 -- 61}, year = {1994}, language = {en} } @article{Schmidt1998, author = {Schmidt, Frank}, title = {Computation of Discrete Transparent Boundary Conditions for the 2D Helmholtz equation}, series = {Optical and Quantum Electronics}, volume = {30}, journal = {Optical and Quantum Electronics}, number = {5,6}, pages = {427 -- 441}, year = {1998}, language = {en} } @inproceedings{Schmidt1998, author = {Schmidt, Frank}, title = {Simulation of Scattering and Reflection Problems via Solution of the 2D Helmholtz Equation}, series = {Integrated Photonics Research}, volume = {4}, booktitle = {Integrated Photonics Research}, pages = {408 -- 410}, year = {1998}, language = {en} } @article{Schmidt1999, author = {Schmidt, Frank}, title = {Construction of Discrete Transparent Boundary Conditions for Schr{\"o}dinger-Type equations}, series = {Surv. Math. Ind.}, volume = {9}, journal = {Surv. Math. Ind.}, pages = {87 -- 100}, year = {1999}, language = {en} } @article{RichterSchlosserSchothetal.2012, author = {Richter, Marten and Schlosser, Felix and Schoth, Mario and Burger, Sven and Schmidt, Frank and Knorr, Andreas and Mukamel, Shaul}, title = {Reconstruction of the wave functions of coupled nanoscopic emitters using a coherent optical technique}, series = {Phys. Rev. B}, volume = {86}, journal = {Phys. Rev. B}, doi = {10.1103/PhysRevB.86.085308}, pages = {085308}, year = {2012}, language = {en} } @inproceedings{RozovaPomplunZschiedrichetal.2012, author = {Rozova, Maria and Pomplun, Jan and Zschiedrich, Lin and Schmidt, Frank and Burger, Sven}, title = {3D finite element simulation of optical modes in VCSELs}, series = {Proc. SPIE}, volume = {8255}, booktitle = {Proc. SPIE}, doi = {10.1117/12.906372}, pages = {82550K}, year = {2012}, language = {en} } @article{RuprechtSchaedleSchmidtetal.2008, author = {Ruprecht, Daniel and Sch{\"a}dle, Achim and Schmidt, Frank and Zschiedrich, Lin}, title = {Transparent boundary conditions for time-dependent problems}, series = {SIAM J. Sci. Comput.}, volume = {30}, journal = {SIAM J. Sci. Comput.}, number = {5}, doi = {10.1137/070692637}, pages = {2358 -- 2385}, year = {2008}, language = {en} } @inproceedings{BurgerZschiedrichSchaedleetal.2006, author = {Burger, Sven and Zschiedrich, Lin and Sch{\"a}dle, Achim and Klose, Roland and Kettner, Benjamin and Pomplun, Jan and Pollok, T. and Schmidt, Frank}, title = {Advanced FEM Analysis of Nano-Optical Devices}, series = {Proc. Symposium on Photonics Technologies for the 7th Framework Programme}, booktitle = {Proc. Symposium on Photonics Technologies for the 7th Framework Programme}, year = {2006}, language = {en} } @inproceedings{BurgerZschiedrichSchmidtetal.2007, author = {Burger, Sven and Zschiedrich, Lin and Schmidt, Frank and K{\"o}hle, Roderick and Henkel, Thomas and K{\"u}chler, Bernd and N{\"o}lscher, Christoph}, title = {3D simulations of electromagnetic fields in nanostructures using the time-harmonic finite-element method}, series = {Modeling Aspects in Optical Metrology}, volume = {6617}, booktitle = {Modeling Aspects in Optical Metrology}, editor = {Bosse, Harald}, publisher = {Proc. SPIE}, doi = {10.1117/12.726236}, pages = {66170V}, year = {2007}, language = {en} } @inproceedings{BurgerZschiedrichSchmidtetal.2007, author = {Burger, Sven and Zschiedrich, Lin and Schmidt, Frank and K{\"o}hle, Roderick and K{\"u}chler, Bernd and N{\"o}lscher, Christoph}, title = {EMF Simulations of Isolated and Periodic 3D Photomask Patterns}, series = {Photomask Technology}, volume = {6730}, booktitle = {Photomask Technology}, publisher = {Proc. SPIE}, pages = {6630}, year = {2007}, language = {en} } @inproceedings{BurgerZschiedrichSchmidtetal.2008, author = {Burger, Sven and Zschiedrich, Lin and Schmidt, Frank and Evanschitzky, Peter and Erdmann, Andreas}, title = {Benchmark of rigorous methods for electromagnetic field simulation}, series = {Photomask Technology}, volume = {7122}, booktitle = {Photomask Technology}, editor = {Kawahira, H. and Zurbrick, L. S.}, publisher = {Proc. SPIE}, doi = {10.1117/12.801248}, pages = {71221}, year = {2008}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2011, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank}, title = {Rigorous simulations of 3D patterns on extreme ultraviolet lithography masks}, series = {Modelling Aspects in Optical Metrology III}, volume = {8083}, booktitle = {Modelling Aspects in Optical Metrology III}, editor = {Bodermann, Bernd}, publisher = {Proc. SPIE}, doi = {10.1117/12.889831}, pages = {80831B}, year = {2011}, language = {en} } @inproceedings{BurgerPomplunSchmidtetal.2011, author = {Burger, Sven and Pomplun, Jan and Schmidt, Frank and Zschiedrich, Lin}, title = {Finite-element method simulations of high-Q nanocavities with 1D photonic bandgap}, series = {Physics and Simulation of Optoelectronic Devices XIX}, volume = {7933}, booktitle = {Physics and Simulation of Optoelectronic Devices XIX}, publisher = {Proc. SPIE}, doi = {10.1117/12.875044}, pages = {79330T}, year = {2011}, language = {en} }